Check Nonlinear Distortion With A Vector Signal Analyzer

Versatile vector signal analyzers can be used to study distortion on burst signals from base stations even while the mobile radio network is still operational.

Nonlinear distortion is a critical performance parameter for power amplifiers in mobile radio networks. Excessive distortion can degrade bit-error-rate (BER) performance, resulting in poor network voice and data transmission. Fortunately, the vector signal analyzer is an instrument designed not only for precise detection of vector and scalar modulation errors, such as error-vector-magnitude (EVM) characteristics, but also for the evaluation of amplifier and system-distortion characteristics. Since the analyzer does not require any special conditions or test signals for effective measurements, the instrument can be used to analyze burst signals from base stations while the mobile radio network is operational.

Traditionally, two-tone or multitone methods1 were used with a selective voltmeter or a spectrum analyzer to determine the compression point of a device under test (DUT). Network analyzers allow similar approaches using power sweeps.2 These methods employ test signals with little relation to "real-world" signals, or signals that are only optimized to the spectral bandwidth or the statistical signal distribution.

Vector signal analyzers are used to measure the scalar and vector modulation parameters and modulation errors of digitally modulated mobile radio signals. Modern concepts enable these instruments to be used for measuring and evaluating linearity errors as well, since all necessary data are collected during the course of normal measurements.3 In fact, a standard test setup can be used without additional measuring instruments or special test signals.

Figure 1 shows a typical test setup for measurements using a vector signal analyzer. A signal generator with in-phase/quadrature (I/Q) modulation capabilities generates an RF mobile radio signal and applies it to the input of the DUT, for example a mobile radio output amplifier. The output of the amplifier is connected to the input of a vector signal analyzer (e.g., a model FSQ-K70 from Rohde & Schwarz) via an attenuator (to avoid unacceptably high levels).This setup allows measurements even directly at the RF output of a base station.

Figure 2 shows a block diagram of a vector signal analyzer. The digitally modulated RF input signal passes through RF and intermediate-frequency (IF) stages (blocks 1 and 2 in Fig. 2) on its way to the input of the analog-to-digital converter (block 3 in Fig. 2). The IF signal is sampled, digitally mixed into a complex baseband signal (block 4 in Fig. 2), digitally filtered (block 5), and stored in random-access memory (block 6).

A digital-signal processor (DSP) demodulates the baseband signals down to the bit level (block 7 in Fig. 2) and generates a "reference signal" corresponding to the undistorted transmit signal. The signal analyzer only needs to know the modulation scheme and appropriate filtering (block 8). After correcting for center-frequency offset, phase, and symbol timing (the synchronization block 9 in Fig. 2), the measured signal is fitted to the reference signal in magnitude and phase (block 10) in order to achieve a root-mean-square (RMS) value of the EVM. In the final stage, the measured signal and the reference signal are compared (block 11 of Fig. 2). Typical modulation errors, such as magnitude error versus time or phase error versus time are then calculated. These signals are used, for example, to display the vector and constellation diagrams or to subsequently calculate the distortion characteristics.

Figure 3(a) shows the ideal constellation diagram of an undistorted raised-cosine-filtered 16-state quadrature-amplitude-modulation (16QAM) signal. Figure 3(b) shows the output signal of an amplifier with pure amplitude distortion. Both figures display vector diagrams for complex baseband signals. The actual constellation points are adjacent to their ideal positions. The curvature of the grid lines is a definite indication of nonlinear, modulation-dependent amplitude distortion. A section of the amplitude time characteristic can be seen in Fig. 3(c). The ideal signal appears as a blue curve while the real signal is shown as a red curve. Symbol times are marked by squares or circles for ease of identification. The three amplitude stages of the ideal signal are indicated by the horizontal lines R1 to R3, and those for the measurement signal are shown by the lines D1 to D3.

While the ideal and real signals still coincide at the lowest level stage, the deviations become larger with increasing level. If each level sample of the distorted signal and the corresponding sample of the ideal signal are plotted in an x/y diagram, the result is a modulation-dependent amplitude characteristic Fig. 3(d)>. For better orientation, the level stages also appear as lines. The deviation of the characteristic from the diagonal ("linear gain") is a measure of the nonlinear distortions of the amplifier .

A practical representation of the distortion characteristic can be derived from the signal ratio between the real and the ideal signal or the difference signal of their logarithmic values Fig. 3(e)>. If each sample of the difference signals is plotted versus the ideal signal in an x/y diagram Fig. 3(f)>, the result is the AM/AM distortion characteristic (amplitude-dependent amplitude distortion). All measurement points are used for interpolating the characteristic curve. In this representation, the deviation of the characteristic from the horizontal 0-dB line is a measure of the nonlinear distortion . Likewise, the phase errors can be derived as a function of the ideal amplitude in an AM/PM characteristic (amplitude-dependent phase distortion).

During analyzer operation, the ideal signal is reconstructed from the demodulated bits, so no previous knowledge of the transmitted data sequence or the ideal I/Q samples is necessary. The characteristics are determined according to the described scheme by comparing the ideal signal with the measurement signal. As a consequence, the amplifier will be measured in precisely the mode in which it is operated later on.

To compute the modulation error, the analyzer fits the measurement signal in a way that minimizes the RMS of the EVM at symbol times. This type of fitting is prescribed in the common mobile radio standards (e.g., EDGE4).

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Figure 4(a) shows the error signal after the fitting, with the symbol times marked. In the logarithmic representation versus the reference signal, fitting causes a slight vertical shift of the measurement points and the interpolated compression curve .

After interpolation, the compression point is determined using two markers with a fixed horizontal distance of 10 dB between them. The point at which the vertical difference of the markers is 1 dB is determined by shifting the markers on the characteristic curve. The position of the marker (C) then represents the 1-dB compression point Fig. 4(b)>.

Figures 4(c) and 4(d) show a practical measurement of a 16-QAM modulation scheme with raised-cosine transmit filtering. This transmit filtering does not expect a receive filter and automatically results in intersymbol-interference-free (i.e., concentrated) constellation points. Fitting produces the following diagram: the position of the inside constellation points is moved slightly to higher levels. Constellation points with an average level are scaled virtually correctly, while the outside points with a high level are moved slightly inward.

The AM/AM distortion curve of the amplifier is obtained by interpolating all the measurement points . The bottom diagram of Fig. 4(d) shows the AM/PM curve, which is interpolated from the x/y representation of the phase difference versus the level of the ideal signal. Both characteristics are vertically shifted as a result of the fitting, but the differential computation of the compression point always provides the correct numeric value.

This new distortion measurement method can be used with all linear modulation schemes and any type of transmit filters. However, this method requires a measurement signal that is not receive filtered. Any receive filtering with strong band limitation causes the nonlinear effects to be distributed with the filter-impulse response over a number of symbol periods. As a result, the signal characteristic will be corrupted.

To illustrate the new distortion measurement method, a burst signal based on the EDGE mobile radio standard was used as an example. The digital standard EDGE uses a 3¼/8-8PSK modulation scheme. For the transmitter,4 a special filter is defined, which is not intersymbol-interference-free. As part of the example measurement, EDGE bursts were demodulated and the result ranges were aligned according to the position of the synchronization sequence (midamble) and limited to the valid area within the burst (useful part). Thus, the edges and areas outside the burst were not used for the measurement analysis.

For measurements performed on a wideband, bipolar small-signal amplifier (not shown), the vector signal analyzer computed the applied input power from the samples, determined the compression point and phase error and displayed them in absolute scaling. For this amplifier, the computed 1-dB compression point was found to be +10.36 dBm (DUT output level) with a phase distortion of 8.71 deg. Besides these level and phase characteristics, the comparison of the mean power levels and the crest factors (peak to average power) provides further information regarding the distortion behavior of the DUT. These measurements indicate a mean power compression of 0.68 dB and a decrease of the crest factor by 0.82 dB.

State-of-the-art vector signal analyzers make it easy to measure nonlinear distortion characteristics and modulation-dependent compression parameters. The same test setup can be used both for classic vector analysis and distortion measurements. The effectiveness of active predistortion for power amplifiers can be verified directly and not merely deduced from other test parameters such as EVM.